**Learning the Option Greeks**

In the world of options, letters of the Greek alphabet (known as "option Greeks," or simply "the Greeks") are used to describe the changes in option premiums that result from the interplay among the three main factors that affect option pricing: stock price relative to strike price, time until expiration, and volatility. Here are the most commonly used option Greeks.

**Delta **measures how much the option's price will change for each 1-point move in the underlying stock. So, a call option with a delta of 0.25, or 25%, indicates the option will gain 25 cents for every one dollar the underlying stock gains. Calls have positive deltas, since they gain in value as the stock rises, while puts have negative deltas, as these contracts will lose value as the stock rises.

Generally speaking, an option's delta is thought to correspond with its chances of finishing in the money at expiration -- so a call option with a delta of 0.85, or 85%, is said to have an 85% chance of being in-the-money at expiration.

Delta is also known as the "hedge ratio," since more sophisticated investors often use this metric to determine how to hedge their long and short investments. For example, if you sell to open one call option with a delta of 50%, you might choose to hedge half of your short stock exposure by purchasing 50 shares of the underlying equity.

**Gamma** is a second-order derivative, as it reflects the unit change in the delta for each 1-point change in the price of the underlying stock. For example, let's say the 55-strike call option for a stock trading at $60 has a gamma of 0.05. The delta is 0.75, or 75%. In this scenario, a $1 rise in the stock price to $61 will push the delta up 0.05 point, or 5 percentage points, to 80%.

For the option buyer, gamma is always positive on both calls and puts. Conversely, for the option seller, the gamma of both calls and puts is always negative. Gamma is highest for options that are at the money, since the delta of these options fluctuates the most as the stock price ticks higher or lower.

**Rho **represents the sensitivity of an option to a change in interest rates. Since there's not a lot of day-to-day volatility in interest rates, rho typically has a somewhat negligible impact on most option trades.

**Theta **gauges the time value of an option. Theta defines the loss in value an option will experience as time passes, and it's usually expressed on a per-day basis. Buying premium will result in a negative theta, because time is working against you, while selling premium involves a positive theta, since the passage of time works in your favor.

So, a long option with a theta of -0.10 will lose about 10 cents per day in value, assuming the stock price and volatility are constant. Theta is non-linear, because it accelerates as the option gets closer to expiration. This rate of decay is proportional to the square root of the time remaining before expiration.

**Vega **measures the change in the option price relative to a change in the option's implied volatility, and it's expressed in dollar terms. An option with a vega of 0.25 will change by 25 cents for every percentage-point change in the implied volatility.

Long calls and puts have positive vega, while short calls and puts have negative vega. These volatility changes are not absolute, though -- they'll have a lesser impact on the price of longer-term options, as well as far out-of-the-money or deep in-the-money options, and options with little time until expiration.

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